Implications, coimplications and left semi-uninorms on a complete lattice

Document Type : Research Paper

Authors

1 College of Information Engineering, Yancheng Teachers University, Jiangsu 224002, People's Republic of China

2 School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu 224002, People's Republic of China

Abstract

In this paper, we firstly show that the $N$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $\vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $N$-dual operation. As a dual result, the $N$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $\wedge$-distributive left semi-uninorm, is the right residual implication induced by its $N$-dual operation. Then, we demonstrate that the $N$-dual operations of the left semi-uninorms induced by an implication and a coimplication, which satisfy the neutrality principle, are the left semi-uninorms. Finally, we reveal the relationships between conjunctive right arbitrary $\vee$-distributive left semi-uninorms induced by implications and disjunctive right arbitrary $\wedge$-distributive left semi-uninorms induced by coimplications, where both implications and coimplications satisfy the neutrality principle.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 14, Issue 1 - Serial Number 1
January and February 2017
Pages 115-130

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